Distorsion of a sphere [Distorsion d'une sphère].




A tridimensional object is defined as a set of points P={X,Y,Z}. To each point P is associated the following pseudo-octonion O={X,Y,Z,0,0,0,0,0}. Then each pseudo-octonion O is submitted to the transformation: 
                                   e2
                                A.O   + B
                    O --> O' = -----------
                                   e1
                                C.O   + D
with {e1,e2} being two arbitrary real numbers and {A,B,C,D} four arbitrary pseudo-octonions.

At last a new point P' is defined with {X',Y',Z'} being arbitrary linear combinations of the components of O'. The set of points P' defines a new tridimensional object...


Nota: the radius and the colors of each particle visualizing a point P' vary according to its {X',Y',Z'} coordinates...


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